// SPDX-License-Identifier: GPL-2.0-or-later
/* mpihelp-div.c  -  MPI helper functions
 *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
 *	Copyright (C) 1998, 1999 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 *	 The GNU MP Library itself is published under the LGPL;
 *	 however I decided to publish this code under the plain GPL.
 */
#include "count_zeros.h"
#include "longlong.h"

#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif

mpi_limb_t mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
                         mpi_limb_t divisor_limb)
{
    mpi_size_t i;
    mpi_limb_t n1, n0, r;
    mpi_limb_t dummy;  // __maybe_unused;

    /* Botch: Should this be handled at all?  Rely on callers?	*/
    if (!dividend_size) return 0;

    /* If multiplication is much faster than division, and the
     * dividend is large, pre-invert the divisor, and use
     * only multiplications in the inner loop.
     *
     * This test should be read:
     *	 Does it ever help to use udiv_qrnnd_preinv?
     *	   && Does what we save compensate for the inversion overhead?
     */
    if (UDIV_TIME > (2 * UMUL_TIME + 6) &&
        (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
        int normalization_steps;

        normalization_steps = count_leading_zeros(divisor_limb);
        if (normalization_steps) {
            mpi_limb_t divisor_limb_inverted;

            divisor_limb <<= normalization_steps;

            /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
             * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
             * most significant bit (with weight 2**N) implicit.
             *
             * Special case for DIVISOR_LIMB == 100...000.
             */
            if (!(divisor_limb << 1))
                divisor_limb_inverted = ~(mpi_limb_t)0;
            else
                udiv_qrnnd(divisor_limb_inverted, dummy, -divisor_limb, 0,
                           divisor_limb);

            n1 = dividend_ptr[dividend_size - 1];
            r  = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

            /* Possible optimization:
             * if (r == 0
             * && divisor_limb > ((n1 << normalization_steps)
             *		       | (dividend_ptr[dividend_size - 2] >> ...)))
             * ...one division less...
             */
            for (i = dividend_size - 2; i >= 0; i--) {
                n0 = dividend_ptr[i];
                UDIV_QRNND_PREINV(
                    dummy, r, r,
                    ((n1 << normalization_steps) |
                     (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                    divisor_limb, divisor_limb_inverted);
                n1 = n0;
            }
            UDIV_QRNND_PREINV(dummy, r, r, n1 << normalization_steps,
                              divisor_limb, divisor_limb_inverted);
            return r >> normalization_steps;
        } else {
            mpi_limb_t divisor_limb_inverted;

            /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
             * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
             * most significant bit (with weight 2**N) implicit.
             *
             * Special case for DIVISOR_LIMB == 100...000.
             */
            if (!(divisor_limb << 1))
                divisor_limb_inverted = ~(mpi_limb_t)0;
            else
                udiv_qrnnd(divisor_limb_inverted, dummy, -divisor_limb, 0,
                           divisor_limb);

            i = dividend_size - 1;
            r = dividend_ptr[i];

            if (r >= divisor_limb)
                r = 0;
            else
                i--;

            for (; i >= 0; i--) {
                n0 = dividend_ptr[i];
                UDIV_QRNND_PREINV(dummy, r, r, n0, divisor_limb,
                                  divisor_limb_inverted);
            }
            return r;
        }
    } else {
        if (UDIV_NEEDS_NORMALIZATION) {
            int normalization_steps;

            normalization_steps = count_leading_zeros(divisor_limb);
            if (normalization_steps) {
                divisor_limb <<= normalization_steps;

                n1 = dividend_ptr[dividend_size - 1];
                r  = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

                /* Possible optimization:
                 * if (r == 0
                 * && divisor_limb > ((n1 << normalization_steps)
                 *		   | (dividend_ptr[dividend_size - 2] >> ...)))
                 * ...one division less...
                 */
                for (i = dividend_size - 2; i >= 0; i--) {
                    n0 = dividend_ptr[i];
                    udiv_qrnnd(
                        dummy, r, r,
                        ((n1 << normalization_steps) |
                         (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                        divisor_limb);
                    n1 = n0;
                }
                udiv_qrnnd(dummy, r, r, n1 << normalization_steps,
                           divisor_limb);
                return r >> normalization_steps;
            }
        }
        /* No normalization needed, either because udiv_qrnnd doesn't require
         * it, or because DIVISOR_LIMB is already normalized.
         */
        i = dividend_size - 1;
        r = dividend_ptr[i];

        if (r >= divisor_limb)
            r = 0;
        else
            i--;

        for (; i >= 0; i--) {
            n0 = dividend_ptr[i];
            udiv_qrnnd(dummy, r, r, n0, divisor_limb);
        }
        return r;
    }
}

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
 * the NSIZE-DSIZE least significant quotient limbs at QP
 * and the DSIZE long remainder at NP.	If QEXTRA_LIMBS is
 * non-zero, generate that many fraction bits and append them after the
 * other quotient limbs.
 * Return the most significant limb of the quotient, this is always 0 or 1.
 *
 * Preconditions:
 * 0. NSIZE >= DSIZE.
 * 1. The most significant bit of the divisor must be set.
 * 2. QP must either not overlap with the input operands at all, or
 *    QP + DSIZE >= NP must hold true.	(This means that it's
 *    possible to put the quotient in the high part of NUM, right after the
 *    remainder in NUM.
 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
 */

mpi_limb_t mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs, mpi_ptr_t np,
                          mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
{
    mpi_limb_t most_significant_q_limb = 0;

    switch (dsize) {
        case 0:
            /* We are asked to divide by zero, so go ahead and do it!  (To make
               the compiler not remove this statement, return the value.)  */
            /*
             * existing clients of this function have been modified
             * not to call it with dsize == 0, so this should not happen
             */
            return 1 / dsize;

        case 1: {
            mpi_size_t i;
            mpi_limb_t n1;
            mpi_limb_t d;

            d  = dp[0];
            n1 = np[nsize - 1];

            if (n1 >= d) {
                n1 -= d;
                most_significant_q_limb = 1;
            }

            qp += qextra_limbs;
            for (i = nsize - 2; i >= 0; i--)
                udiv_qrnnd(qp[i], n1, n1, np[i], d);
            qp -= qextra_limbs;

            for (i = qextra_limbs - 1; i >= 0; i--)
                udiv_qrnnd(qp[i], n1, n1, 0, d);

            np[0] = n1;
        } break;

        case 2: {
            mpi_size_t i;
            mpi_limb_t n1, n0, n2;
            mpi_limb_t d1, d0;

            np += nsize - 2;
            d1 = dp[1];
            d0 = dp[0];
            n1 = np[1];
            n0 = np[0];

            if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
                sub_ddmmss(n1, n0, n1, n0, d1, d0);
                most_significant_q_limb = 1;
            }

            for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
                mpi_limb_t q;
                mpi_limb_t r;

                if (i >= qextra_limbs)
                    np--;
                else
                    np[0] = 0;

                if (n1 == d1) {
                    /* Q should be either 111..111 or 111..110.  Need special
                     * treatment of this rare case as normal division would
                     * give overflow.  */
                    q = ~(mpi_limb_t)0;

                    r = n0 + d1;
                    if (r < d1) { /* Carry in the addition? */
                        add_ssaaaa(n1, n0, r - d0, np[0], 0, d0);
                        qp[i] = q;
                        continue;
                    }
                    n1 = d0 - (d0 != 0 ? 1 : 0);
                    n0 = -d0;
                } else {
                    udiv_qrnnd(q, r, n1, n0, d1);
                    umul_ppmm(n1, n0, d0, q);
                }

                n2 = np[0];
            q_test:
                if (n1 > r || (n1 == r && n0 > n2)) {
                    /* The estimated Q was too large.  */
                    q--;
                    sub_ddmmss(n1, n0, n1, n0, 0, d0);
                    r += d1;
                    if (r >= d1) /* If not carry, test Q again.  */
                        goto q_test;
                }

                qp[i] = q;
                sub_ddmmss(n1, n0, r, n2, n1, n0);
            }
            np[1] = n1;
            np[0] = n0;
        } break;

        default: {
            mpi_size_t i;
            mpi_limb_t dX, d1, n0;

            np += nsize - dsize;
            dX = dp[dsize - 1];
            d1 = dp[dsize - 2];
            n0 = np[dsize - 1];

            if (n0 >= dX) {
                if (n0 > dX || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
                    mpihelp_sub_n(np, np, dp, dsize);
                    n0                      = np[dsize - 1];
                    most_significant_q_limb = 1;
                }
            }

            for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
                mpi_limb_t q;
                mpi_limb_t n1, n2;
                mpi_limb_t cy_limb;

                if (i >= qextra_limbs) {
                    np--;
                    n2 = np[dsize];
                } else {
                    n2 = np[dsize - 1];
                    MPN_COPY_DECR(np + 1, np, dsize - 1);
                    np[0] = 0;
                }

                if (n0 == dX) {
                    /* This might over-estimate q, but it's probably not worth
                     * the extra code here to find out.  */
                    q = ~(mpi_limb_t)0;
                } else {
                    mpi_limb_t r;

                    udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
                    umul_ppmm(n1, n0, d1, q);

                    while (n1 > r || (n1 == r && n0 > np[dsize - 2])) {
                        q--;
                        r += dX;
                        if (r < dX) /* I.e. "carry in previous addition?" */
                            break;
                        n1 -= n0 < d1;
                        n0 -= d1;
                    }
                }

                /* Possible optimization: We already have (q * n0) and (1 * n1)
                 * after the calculation of q.  Taking advantage of that, we
                 * could make this loop make two iterations less.  */
                cy_limb = mpihelp_submul_1(np, dp, dsize, q);

                if (n2 != cy_limb) {
                    mpihelp_add_n(np, np, dp, dsize);
                    q--;
                }

                qp[i] = q;
                n0    = np[dsize - 1];
            }
        }
    }

    return most_significant_q_limb;
}

/****************
 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
 * Return the single-limb remainder.
 * There are no constraints on the value of the divisor.
 *
 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
 */

mpi_limb_t mpihelp_divmod_1(mpi_ptr_t quot_ptr, mpi_ptr_t dividend_ptr,
                            mpi_size_t dividend_size, mpi_limb_t divisor_limb)
{
    mpi_size_t i;
    mpi_limb_t n1, n0, r;
    mpi_limb_t dummy;  // __maybe_unused;

    if (!dividend_size) return 0;

    /* If multiplication is much faster than division, and the
     * dividend is large, pre-invert the divisor, and use
     * only multiplications in the inner loop.
     *
     * This test should be read:
     * Does it ever help to use udiv_qrnnd_preinv?
     * && Does what we save compensate for the inversion overhead?
     */
    if (UDIV_TIME > (2 * UMUL_TIME + 6) &&
        (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
        int normalization_steps;

        normalization_steps = count_leading_zeros(divisor_limb);
        if (normalization_steps) {
            mpi_limb_t divisor_limb_inverted;

            divisor_limb <<= normalization_steps;

            /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
             * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
             * most significant bit (with weight 2**N) implicit.
             */
            /* Special case for DIVISOR_LIMB == 100...000.  */
            if (!(divisor_limb << 1))
                divisor_limb_inverted = ~(mpi_limb_t)0;
            else
                udiv_qrnnd(divisor_limb_inverted, dummy, -divisor_limb, 0,
                           divisor_limb);

            n1 = dividend_ptr[dividend_size - 1];
            r  = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

            /* Possible optimization:
             * if (r == 0
             * && divisor_limb > ((n1 << normalization_steps)
             *		       | (dividend_ptr[dividend_size - 2] >> ...)))
             * ...one division less...
             */
            for (i = dividend_size - 2; i >= 0; i--) {
                n0 = dividend_ptr[i];
                UDIV_QRNND_PREINV(
                    quot_ptr[i + 1], r, r,
                    ((n1 << normalization_steps) |
                     (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                    divisor_limb, divisor_limb_inverted);
                n1 = n0;
            }
            UDIV_QRNND_PREINV(quot_ptr[0], r, r, n1 << normalization_steps,
                              divisor_limb, divisor_limb_inverted);
            return r >> normalization_steps;
        } else {
            mpi_limb_t divisor_limb_inverted;

            /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
             * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
             * most significant bit (with weight 2**N) implicit.
             */
            /* Special case for DIVISOR_LIMB == 100...000.  */
            if (!(divisor_limb << 1))
                divisor_limb_inverted = ~(mpi_limb_t)0;
            else
                udiv_qrnnd(divisor_limb_inverted, dummy, -divisor_limb, 0,
                           divisor_limb);

            i = dividend_size - 1;
            r = dividend_ptr[i];

            if (r >= divisor_limb)
                r = 0;
            else
                quot_ptr[i--] = 0;

            for (; i >= 0; i--) {
                n0 = dividend_ptr[i];
                UDIV_QRNND_PREINV(quot_ptr[i], r, r, n0, divisor_limb,
                                  divisor_limb_inverted);
            }
            return r;
        }
    } else {
        if (UDIV_NEEDS_NORMALIZATION) {
            int normalization_steps;

            normalization_steps = count_leading_zeros(divisor_limb);
            if (normalization_steps) {
                divisor_limb <<= normalization_steps;

                n1 = dividend_ptr[dividend_size - 1];
                r  = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

                /* Possible optimization:
                 * if (r == 0
                 * && divisor_limb > ((n1 << normalization_steps)
                 *		   | (dividend_ptr[dividend_size - 2] >> ...)))
                 * ...one division less...
                 */
                for (i = dividend_size - 2; i >= 0; i--) {
                    n0 = dividend_ptr[i];
                    udiv_qrnnd(
                        quot_ptr[i + 1], r, r,
                        ((n1 << normalization_steps) |
                         (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                        divisor_limb);
                    n1 = n0;
                }
                udiv_qrnnd(quot_ptr[0], r, r, n1 << normalization_steps,
                           divisor_limb);
                return r >> normalization_steps;
            }
        }
        /* No normalization needed, either because udiv_qrnnd doesn't require
         * it, or because DIVISOR_LIMB is already normalized.
         */
        i = dividend_size - 1;
        r = dividend_ptr[i];

        if (r >= divisor_limb)
            r = 0;
        else
            quot_ptr[i--] = 0;

        for (; i >= 0; i--) {
            n0 = dividend_ptr[i];
            udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb);
        }
        return r;
    }
}
